Mathematical Research Letters

Volume 5 (1998)

Number 4

Supersimple fields and division rings

Pages: 473 – 483

DOI: http://dx.doi.org/10.4310/MRL.1998.v5.n4.a5

Authors

A. Pillay (UIUC)

T. Scanlon (University of California at Berkeley)

F. O. Wagner (Maths. Institute, Oxford)

Abstract

It is proved that any supersimple field has trivial Brauer group, and more generally that any supersimple division ring is commutative. As prerequisites we prove several results about generic types in groups and fields whose theory is simple.